According
to [1]}, [2]},
we equip the virtual element edge space \(\mathbf {V}_{h}^{\operatorname{edge}}\)  with an inner
product mimicking the \(L^{2}\)  inner product.
Notably, we first introduce the local bilinear form
\(\big [\mathbf {E}_{h},\mathbf {F}_{h}\big ]_{\operatorname{edge},K} :=\Big (\Pi ^{0,K}_{0}\mathbf {E}_{h},\Pi ^{0,K}_{0}\mathbf {F}_{h}\Big )_{K} +S^{K}_{\operatorname{edge}}\Big ( (I-\Pi ^{0,K}_{0})\mathbf {E}_{h}, (I-\Pi ^{0,K}_{0})\mathbf {F}_{h}\Big )\\\forall \mathbf {E}_{h},\,\mathbf {F}_{h}\in \mathbf {V}_{h}^{\operatorname{edge}}(K),\) 
